6. RESULTS AND DISCUSSION
6.3.2. Analysis and modelling of EIS data
EIS along with electrical equivalent circuit analysis was applied within the range of −2.28 to −0.83 V for the Bi(hkl)│PMImI systems.
Figure 27. Electrical equivalent circuit used for the fitting of the impedance data.
EIS EC fitting process has been applied to the Bi(hkl)│PMImI systems and an equivalent circuit has been derived, shown in Fig. 27. It should be noted that not all components of the EC can be quantified within the whole frequency and potential ranges measured and thus some components have been omitted when the role of the process that they correspond to is too small. Overall, the EC is described by 6 elements corresponding to 7 free parameters denoting a system with two time-constants. RS corresponds to the solution resistance which describes the overall electric resistance as well as the solution layer resistance
between the electrode and Luggin capillary. This parameter should not strongly depend on the potential applied if the resistance of the dielectric medium is constant. Rads corresponds to the resistance of the specific adsorption process of iodide ions on the Bi electrode surface. This parameter should decrease when more positive electrode potential is applied. In parallel with the adsorption resistance Warburg like semifinite-length diffusion element Wo describes the mass-transfer limited movement of adsorbing ionic species in a thin interface layer. This element is required because of the high viscosity and low diffusion coefficient [62] of the PMImI ionic liquid ions. The mass-transfer limited element is used in the classical form with the value of α fixed at 0.5 and is thus described by two free parameters: mass-transfer resistance RD and mass-transfer time constant Twar that describes the time taken for the diffusing particles to move through the thin layer. This means that by knowing the diffusion constant of relevant species, the thickness of the thin layer can be evaluated [144]. In series with both the mass-transfer and adsorption resistance components is the electrical double layer capacitance Cdl. This is the primary component whereby the capacitive charge storage of the system can be evaluated.
Two additional elements in parallel with the previous three components describe the low-frequency end of the impedance spectrum, as shown in Fig. 27.
Charge-transfer resistance, Rct, characterises faradic charge transfer processes involving either low-concentration impurities or the ions of the ionic liquid themselves. This element can describe many different reactions that take place at different potential values, but will always primarily describe the fastest process taking place at a selected fixed potential. Thus, at the most negative potential region, it will show the reduction of PMIm+ cations and at the positive potential region show the oxidation of iodide ions. If the process ascribed by the Rct component is either reversible or quasi-reversible, the pseudo-capacitive term, Cpseudo, is added in series with Rct to evaluate the energy storage ability of the faradic reaction. Again, although this term should be evaluated in terms of capacity, the parameter is still shown in capacitance units (thus the name- capacitance-like). This element is not used at more negative potentials (E <
−1.1 V) as the reactions taking place at more negative potentials are not reversible.
Figure 28. Electrical double layer capacitance Cdl vs. E dependence for the Bi(hkl)│PMImI systems (a) and cut-out of the electrostatic double layer potential range (inset a); series capacitance CS vs. E dependence for the Bi(hkl)│0.1 M KI aqueous electrolyte systems (b).
The electrical double layer capacitance for the Bi(hkl)│PMImI systems, obtained from EC fitting results, are shown in Fig. 28a. Each of the EC fitting parameters carries with it an error value based on the goodness of fit for that specific parameter. It is seen that the error values for the Cdl parameter are extremely low and thus almost unnoticeable in the figure. The negative-potential region cut-out of the same graph is shown in the inset of Fig. 28a. It is seen that the data can be divided into two distinct areas of more and less negative electrode potential. In the more negative electrode potential region from −2.3 to approximately −1.4 V the value of capacitance is relatively low (between 12 and 25 μF cm−2) and the general behaviour of the three electrodes is similar. However, one can still easily detect that the capacitance of the most metallic Bi(011̅) plane is appreciatively higher than that of the least metallic Bi(111) plane (17 vs. 14 μF cm−2 in the potential region from −2.3 to −1.7 V) while the Bi(001) plane with average metallic character fits between the previous two planes. Thus the capacitance follows the same general rule as that observed for aqueous electrolytes, whereby higher metallicity of the electrode material correlates well with the double layer capacitance response of the dense layer [145]. This is of great interest because such general trend, based on the available literature, is not followed in case of perceived surface inactive ionic liquid EMImBF4, whereby the average double layer capacitance at the minimum decreases in the order of Sb(111) [146] > Bi(111) [147] ~ Hg(liquid) [148] > Cd(0001) [149]. It is unknown as to how one might explain such difference for metal electrodes. However, the same effect does not apply for carbon based materials (perceived as least metallic) that show capacitance
significantly lower than that of metals [56,143], clearly limited by their charge carrier concentration at a given potential. If such an effect is indeed true, it would signify that carrier concentration is not the primary limiting factor in the screening of the double layer electric field for most metals in an ionic liquid media. Clearly, this is not the case for our Bi(hkl) single crystal planes whereby metallicity is important to consider even in the electrostatic double layer region.
Even more interesting is the potential range from −1.3 to −0.8 V, where the difference in the double layer capacitance response for the three Bi electrodes is more pronounced. Whereas the most semi-metallic Bi(111) plane shows a relatively constant increase of capacitance in this region with a maximum of about 55 μF cm−2, the more metallic (001) and (011) planes show a significantly sharper increase of capacitance and maxima of 115 and 87 μF cm−2 have been measured, respectively. This effect is perceived to be the result of the inter-action between the electronic and ionic surface structure, resulting from partial charge transfer from the iodide ions of the electrolyte to conduction band of the Bi(hkl) electrode. Because each single crystal plane has a distinct surface electronic structure, this effect is more pronounced for electrodes with higher number of free electronic states (metals) and less pronounced for semi-metals with a relatively low concentration of valence electronic states. In the case of the three Bi single crystal electrodes that are all semi-metallic in nature with a varying degree of metallicity, the measurement of capacitance clearly shows the difference between the three different planes and provides information about the relative band structure of each electrode.
In order better understand this effect of electronic capacitance on the overall capacitance response, the same three Bi single crystals were measured in a more typical, 0.1 M KI aqueous electrolyte solution [69,70]. The series capacitance results of the Bi(hkl)│0.1M KI in H2O measured at 210 Hz are shown in Fig.
28b. It should be noted that although the single frequency series capacitance results are less accurate than EC fitting of the Cdl element, they can still well represent the EDL capacitance if the frequency value at which they are measured is well-chosen. The chosen CS ac frequency is significantly higher for the aqueous electrolyte solution because of the differences in viscosity and conductivity between the two electrolytes. As observed by comparing the C, E curves in Fig. 28 a and b, many similarities are found. The C, E curve for the KI system can also be generally divided into two parts of differing capacitance behaviour, and the general logic between the three different single crystal planes also holds true. The overall values of the capacitance maxima are up to 50%
larger for the aqueous electrolyte compared to PMImI ionic liquid, but is compensated by the narrower electrochemical stability range, meaning that the absolute surface charge density values are similar. It is also evident that the C, E curves for the least metallic Bi(111) plane are most similar between the PMImI and 0.1M KI in H2O electrolytes with only 10% difference between the capacitance maxima and comparable linear increase of capacitance in the less negative potential range, where the specific adsorption of iodide ions has been observed. The most likely explanation for this effect is that the C,E curves are
mainly limited by the electronic response of the electrode material and thus behave in a similar manner as that observed for HOPG electrodes [54], whereby the difference between the capacitance response is very small for both electrolyte concentration, solvent or the absence of a solvent. The differences between the more metallic Bi planes are more significant for the two electro-lytes, however, still show general features that are comparable for the PMImI and 0.1M KI electrolytes.
Finally, it is interesting to observe the electrode potential dependence of the resistive components of the EC fitting, shown in Fig. 29. The solution resistance RS is primarily determined by the distance between the working electrode and reference electrode capillary as well as the electrolyte conductivity, both of which are inherently constant for our measurements and should thus reveal no strong dependence of RS on electrode potential. This, however, ignores the possibility of changes in the electrolyte composition under electrochemical polarization, which could have a significant contribution on the overall electro-lyte resistance. It is seen in Fig. 29a that indeed there is no specific dependence of RS on the Bi single crystal plane, as the measurements were conducted in fundamentally the same fashion and the resistance is relatively constant, considering fitting error, within the potential range from −2.3 to −1.2 V.
Thereafter, however, RS starts to decrease rapidly with potential at E > −1.2 V for all Bi electrodes. This effect is again interpreted to stem from the behaviour of iodide ions in a solution. Because of the high viscosity, the diffusion coefficient of iodide ions in the PMImI ionic liquid is very low, about 1.9·10−12 m2 s−1 [62]. However, if molecular iodine were added to the solution, as is the case when the same ionic liquid is used as an electrolyte in a DSSC, triiodide ions would be formed [152]. As is known from literature, in an electrolyte composed of both iodide and triiodide ions the conductivity can be significantly enhanced because of an alternative conduction path the hopping of iodide ions from one complex to another [72]. This mechanism has been shown to have a diffusion coefficient on the order of 10−9 m2 s−1 [62,72], thus 3 orders of magni-tude higher than that of pure iodide in PMImI. At less negative potential (E >
−1.2 V) iodide ions can be oxidized into triiodide ions, as shown by the CV measurements. This can therefore create a parallel conduction mechanism for the electrolyte resistance and it is likely the reason as to why we observe a rapid, linear decrease of the RS parameter for our systems. The overall decrease is up to 8% for the Bi(111) electrode, suggesting that a considerable amount of free triiodide ions have been formed, diffused into the bulk electrolyte and reduced at the counter-electrode.
Figure 29. Calculated fitting parameters of Nyquist plots for the Bi(hkl)│PMImI systems; solution resistance RS (a) and charge-transfer resistance Rct (b) vs. E depen-dence.
The resistance of low frequency charge transfer process (Rct) is shown in Fig.
29b. The process to which this parameter corresponds to changes with applied electrode potential, and from −1.6 V to −1.3 V no significant charge transfer processes are taking place at the Bi(hkl) electrode surface, thus contributing to the high fitting error in this potential region. For potentials more negative than
−2.1 V this process corresponds to the reduction of imidazolium cations [56]
discussed beforehand. Within the potential region from −2.1 to −1.6 V, the reduction of trace water impurities is interpreted to be the main cause of Rct
[147]. At electrode potential values above −1.3 V, Rct characterises the slow redox processes, causing also the quasi-reversible peaks in the CV curves and increase in the values of Cpseudo. No specific dependence of Rct on the Bi(hkl) planes is observed as the faradic resistance of these processes mostly overlap for the three Bi single crystal planes suggesting that the chemical nature of Bi is more influential on these processes compared to both the surface electronic structure and the ionic structure of the EDL, supported by the similarities between the Bi planes in CV and EIS resistance parameters.
6.4. (I-VIII) Considerations of the EDL
Theoretical and modelling approaches have been by far the most proactive in trying to explain the charge screening properties of ionic liquids. A large number of different approaches have been taken, ranging from extensions of the diffuse double layer theory [16,17] up to extensive molecular dynamics (MD) simulations with different electrolyte geometries, electrodes and temperatures
[27–29]. A major drawback to almost all of the MD based studies is the complete exclusion of electronic effects of the EDL, such as the work function difference between the electrode and the electrolyte [14], electronic structure of the electrode, partial charge transfer between ions and the electrode as well as the association of the ions. This is exemplified by the way potential is treated for polarizable and non-polarizable systems [30]. Thus, the results of these theoretical approaches cannot be considered reliable at potentials near the pzc where the discrepancy in electrode│electrolyte work function difference is highest. Most of these models are in general agreement about the capacitive behaviour at high surface charge densities, as they show a slow decrease of capacitance at the potential ‘wings’ (extrema). It can be suggested that at high surface charge density, the strong electric fields are enough to overcome the association between ions within the compact layer and thus a hard spheres approach would be sufficient to characterize the essential physics of the inter-face, however, the limitation of the region of ideal polarizability for EMImBF4 ionic liquid will not allow us to gauge that.
It is thus seen that the consideration of specific interactions (both between the ions and between the ions and the electrode surface) within an IL is extremely important in trying to explain the capacitive behaviour of metal│IL interfaces, which has been exemplified in this thesis. By considering the association between ions in ILs, we are able to explain the results of this study as well as consider many of the discrepancies observed in other experimental and theoretical studies. The results are also in good agreement with different AFM force-distance measurements [122,154] in ILs, showing pseudo-layering at IL interfaces, with layers approximately the thickness of ion pairs. This would suggest that dipole, not coulombic interactions are the most important part of the overall screening response of the electrolyte at low surface charge densities. These pseudo-layers can also be ‘turned around’ in order to screen positive or negative surface charge, and a thickening of the structured electrolyte layer would be consistent with the increase of capacitance relative to the pzc. Nonetheless, as is observed by the SEIRA measurements shown in this study, there is a finite range of electrode potential wherein this consideration is applicable. Because of the strong electric fields at high surface charge densities, the strength of ion association between the ions is seen to decrease considerably and thus the capacitance is also seen to decrease at the wings, giving rise to coulombic screening response of the electrolyte. It can be suggested that at extreme surface charge densities, whereupon all of the ionic association between the ions in the dense layer has been overcome, the description of hard-sphere ILs would be sufficient in explaining the overall capacitance response of the interface.
As it was shown by in situ ER spectroscopy results, the mechanism of energy storage for the dielectric graphite│PDCA system significantly differs from the purely electrostatic graphite│EMImBF4 supercapacitor system [115,143]. Although this is not surprising, the exact mechanism of energy storage in dielectric capacitors, particularly from the view-point of conductor
electronic states, has not, thus far, been revealed. Such knowledge could help us in designing even higher energy density capacitors in the future by careful selection of both electrode materials and electrolyte components [139].
The measurements of specifically adsorbing iodide ions at Bi single crystal planes demonstrate that the capacitance of IL interfaces can be significantly increased via careful selection of electrolyte additives. However, it is also shown that this increase is highest for more metallic planes of semimetal Bi(hkl), thus limiting this effect for carbon based SC materials [155]. It should be noted, though, that these results clearly demonstrate that both the specific adsorption of iodide ions as well as the oxidation of iodide increase the energy storage capabilities of such systems [63].
At last, the shape of the C, E curve for the graphite│EMImBF4 system and potential dependence of the in situ IRA spectra for the same system do not confirm the existence of multiple double layers, suggested by a theoretical article about the interface between graphite and an IL [35]. On the contrary, the experimental results suggest that more comprehensive models are required for a fundamental understanding of the complex processes at the electrode│IL interface.